The long exact sequence is returned as a Net with the following general format:
| .- -> 0 | ( | \ | | \ | .- -> W ** X - - -> W ** X/A - - -> 0 - -' | ( | \ | | \ | .- -> Tor_1(W,X) - - -> Tor_1(W,X/A) - - -> W ** A - -' | ( | \ | | \ | .- -> Tor_2(W,X) - - -> Tor_2(W,X/A) - - -> Tor_1(W,A) - -' | ( | \ | | \ | (k-3) more rows appearing ... - -' |
The next example gives a typical use.
i1 : R = QQ[x] o1 = R o1 : PolynomialRing |
i2 : X = R^1 / x^9
o2 = cokernel | x9 |
1
o2 : R-module, quotient of R
|
i3 : A = image map(X,,{{x^7}})
o3 = subquotient (| x7 |, | x9 |)
1
o3 : R-module, subquotient of R
|
i4 : W = coker map(R^1,,{{x^3}})
o4 = cokernel | x3 |
1
o4 : R-module, quotient of R
|
i5 : TorLES(3,W,X,A)
warning: clearing value of symbol f to allow access to subscripted variables based on it
: debug with expression debug 3406 or with command line option --debug 3406
o5 = .- -> 0
0 (
\
0 \
.- -> cokernel | x3 | - - - -> cokernel | x3 | - - -> 0 - -'
0 ( | 1 |
\
{7} | 1 | \
.- -> cokernel {9} | x3 | - - - - - - -> cokernel {7} | x3 | - - - - - -> cokernel {7} | x2 | - -'
{9} | x |( {7} | x2 |
\
0 \
.- -> 0 - - -> 0 - - -> cokernel {10} | x2 | - -'
0 ( 0
\
\
0 - -'
|
i6 : apply(2, p -> prune Tor_p(W,X))
o6 = {cokernel | x3 |, cokernel {9} | x3 |}
o6 : List
|
i7 : apply(2, p -> prune Tor_p(W,X/A))
o7 = {cokernel | x3 |, cokernel {7} | x3 |}
o7 : List
|
i8 : apply(2, p -> prune Tor_p(W,A))
o8 = {cokernel {7} | x2 |, cokernel {10} | x2 |}
o8 : List
|
For computational access to the maps in the sequence, use TorCouple instead.
The object TorLES is a method function.